[jdh]

Yes, when the screen is off the active application still runs regardless of which application it is. Therefore, OmniFocus syncs.

You'll want to be cautious of this with regards to battery life, since leaving certain apps running, even with the screen off, can have a serious drain on your battery. OF syncing hourly shouldn't be that big of a deal, but other apps such as the Camera app, will kill the battery noticeably faster if left running (since the Camera circuitry remains "active").